EP 0 814 012 B1, for instance, discloses an electric steering booster device incorporating a ball screw drive. In this prior art, an axial extension of a toothed rack comprises a spindle on which a spindle nut is arranged. Balls arranged between the spindle and the spindle nut roll in ball grooves configured on the inner periphery of the spindle nut and the outer periphery of the spindle. These ball grooves define a load-bearing channel in which the balls roll under load. For forming an endless circuit of balls, the spindle nut comprises a so-called external deflector that connects the two ends of the load-bearing channel endlessly to each other. The external deflector winds around approximately 180° about the outer periphery of the spindle nut. At the end of the load-bearing channel that generally comprises several windings, the balls are deflected into the external deflector. Within this deflector, the balls move in the load-free return channel. They are deflected from there to the beginning of the load-bearing channel and roll again along the ball grooves. At its axial ends, the spindle nut is supported radially through a groove ball bearing. Further, a toothed wheel is arranged rotationally fast on the spindle nut and meshes with a drive pinion of an electromotor. The toothed wheel is arranged axially spaced from the external deflector. This arrangement has a considerable design space requirement in axial direction.